Resistance of Fluids. 393 



becomes 



71 SV 2 X 3 71 SV 2 j M 



'1- . . R d a? = - . x* dx; 

 g R' g* 2 



the integral of which, or ^-^- a? 4 , is the resistance to the sphcri- 

 4^R 2 



cal surface generated by BE. And when a; or CF is = R or CA, 

 it becomes 7CSV *'- for the resistance on the whole hemisphere ; 



4# 



which is also equal to n * v . D where D = 2 R, the diameter. 

 103 



(3.) But the perpendicular resistance to the circle of the 

 same diameter D or BD, by section 6 of the preceding problem, is 



71 s v * p2 . which being double the former, shows that the resist- 



*g 

 ance to the sphere is just equal to half the direct resistance to a great 



circle of it, or to a cylinder of the same diameter. 



(4.) Since |#D 3 is" the magnitude of the globe; if s' denote 

 its density or specific gravity, its weight w will be = wD 3 /, 

 and therefore the retarding force 



m __ 7i s v 2 D 2 6 3sv 2 ^ 



* F W ~ l6g~ ' TTS'D 3 "~ SgS* D ' 



which is also equal to 



v 2 



2gs' 

 Hence 



3s l 

 4s^>~ P 

 and 



which is the space that would be described by the globe while 

 its whole motion is generated or destroyed by a constant force 

 equal to the resistance, if no other force acted on the globe to 

 continue its motion. And if the density of the fluid were equal 

 to that of the globe, the resisting force sufficient would be act- 

 ing constantly on the globe without any other force, to generate 

 or destroy the motion while describing the space f D, or of its 

 diameter. 



Mech. 50 



